When writing an equation from a verbal description or word problem, you need to look for clue words and phrases that tell you which operations you should use.
Words such as "and," "together," and "total" suggest that you will need to use addition. Words and phrases such as "product," "times," and "increase by a factor of" indicate that you should use multiplication.
Click on the each mathematical symbol for a list of words or phrases you may see in a problem that tell you to use that operation.
Consider the following situation:
Marta and her family are staying at a campground that charges a non-refundable $15.00 security deposit plus $30.00 for each day that her family stays.
What clue words suggesting operations does the problem use?
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For each → multiply the number of days by $30
Plus → add the product of the number of days and $30 to $15
Write a plan for solving this problem.
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Multiply the number of days that her family stays at the campground by 30, and then add that product to 15.
Write this plan as an equation that could be solved for y, the cost of staying at the campground for x days.
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y = 15 + 30x
Copy the following table into your notes and use your solution plan to fill in the missing information.
| Number of days (x) |
Process | Cost (y) |
| 2 | 15 + 30(2) | $75.00 |
| 3 | ||
| 4 | ||
| 5 | ||
| x |
| Number of days (x) |
Process | Cost (y) |
| 2 | 15 + 30(2) | $75.00 |
| 3 | 15 + 30(3) | $105.00 |
| 4 | 15 + 30(4) | $135.00 |
| 5 | 15 + 30(5) | $165.00 |
| x | 15 + 30(x) | y = 15 + 30x |
How did you fill in the y column?
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Calculate the value for y by using the solution plan with each value for x.
When creating a graph from a verbal description, it is usually best to make a table of values first. Because of this, we will cover the specific concepts of graphing data in more depth in section 3. In this section, we will concentrate on the general properties of the graph of the data.
If Marta's family pays the security deposit, and then due to a change in plans ends up staying 0 nights, how much will they have paid in total?
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They will have paid $15.
Is the cost increasing or decreasing as the number of days increases?
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The cost is increasing.
If you were to graph this data, would you expect the graph to rise or fall as you move to higher x values? Why?
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The graph would rise from left to right because as the number of days spent camping increases, the cost to stay at the campground increases.
In general, how would you describe the graph of the data associated with this problem?
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The first point on the graph would demonstrate that at 0 days, Marta's family would pay $15. The points would rise as you move to the right on the graph to demonstrate that as the number of nights increases, the price increases.
Darius earned a total of $800 mowing lawns over the summer. He wants to buy video games that cost $25.00 each. How can you determine y, the amount of money he will have left if he buys x video games?
Write a plan that you could use to solve this problem.
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Start with 800 and then subtract the product of 25 and the number of games he buys.
Copy the following table into your notes and use your solution plan to fill in the missing information.
| Number of games (x) |
Process | Remaining money (y) |
| 2 | 800 – 25(2) | $750.00 |
| 3 | ||
| 4 | ||
| 5 | ||
| x |
| Number of games (x) |
Process | Remaining money (y) |
| 2 | 800 – 25(2) | $750.00 |
| 3 | 800 – 25(3) | $725.00 |
| 4 | 800 – 25(4) | $700.00 |
| 5 | 800 – 25(5) | $675.00 |
| x | 800 – 25(x) | y = 800 – 25x |
Write your plan as an equation.
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y = 800 – 25x
What would you expect the graph of this data to look like? Why?
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The first point on the graph would demonstrate that with 0 video games, Darius has $800. The points would fall as you move to the right on the graph to demonstrate that as the number of video games increases, the amount of money he has decreases.